Embedding problems for real division algebras

Abstract

By using the well-known processes of isotopy and Cayley-Dickson duplication, we plunge every two-dimensional real division algebra into an algebra isotopic to H and every real division algebra isotopic to H into an algebra isotopic to O. Also these processes permit us to show that every four-dimensional real power commutative division algebra, not necessarily isotopic to H, can be embedded into an eight-dimensional real division algebra which is power commutative. This partially answers a question asked in J. Algebra 282 (2004), 758-796. Such an embedding is refined in a way to provide examples where the triviality of the Lie algebra of derivations is preserved.